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Dispersion relations of mesons in symmetric nuclear matter

We calculate dispersion relations and propagators for the $\sigma$, $\omega$, $\pi$, $\rho$, $\delta$, $\eta$ and $a_1$ mesons in relativistic, dense, hot, symmetric nuclear matter. In addition to the usual mixing of the $\sigma-\omega$ system, we obtain mixing of the $\delta$ with the longitudinal $\rho$ mode and of the tranverse $\rho$ with the transverse $a_1$ mode. Finally, the component of the $a_1$ polarization along the transferred momentum modifies the in-medium pion propagator in a way similar to the Migdal contact interaction, but with the opposite sign. The spurious pion condensate as well as the additional contribution from the $a_1$ meson are removed by a contact term. We compare two ways of implementing contact term subtraction.